After an overview of the stylised facts about Africa's natural resources, we discuss the problems and challenges facing the management of natural resources in Africa. We highlight the paradox of plenty, which is that many resource-rich countries in Africa have bad growth performance. They typically also have low investment rates and high degrees of inequality. The curse is especially bad for point-source resources such as oil, gas and diamonds and less for diffuse resources. We point out on the basis of cross-country evidence that this paradox can be resolved if institutions are good, financial systems well developed and the economy open to international trade. We argue that the quintessential nature of the paradox of plenty arises from the very high volatility of commodity prices. This further strengthens the case for good financial systems. We subsequently focus on an analytical framework for the assessment of the management of natural resource wealth. We point out that rapacious rent seeking and the lack of effective mineral property rights has led to negative genuine saving rates and the gradual erosion of the wealth of many African countries. Although there may be a rationale for negative genuine saving if countries are investing heavily in new innovative exploration technology, this hardly seems the case for Africa. The challenge for policymakers in Africa is therefore how to get more incentive-compatible contracts and transparent accounts of mineral extraction. A key question is how to manage natural resource wealth and whether it should be used to save and invest or to boost purchasing power of the people. If it is spent, the challenge is to spend the resource revenues on productive purposes. We conclude with a discussion of the role of China and India in the new 'scramble' for Africa's natural resources.